Question

Vibrating tuning fork of frequency n is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through 8.75 cm, the intensity of sound changes from a maximum to minimum. If the speed of sound is 350 m/s. Then n is

• A. 500 Hz
• B. 1000 Hz
• C. 2000 Hz
• D. 4000 Hz

Answer 1

The correct option is B

1000 Hz

When the piston is moved through a distance of 8.75cm, the path difference produced is $2\times 8.75cm=17.5cm$. This must be equal to $\frac{\lambda }{2}$ for for a change from maximum to minimum.$\therefore \frac{\lambda }{2}=17.5cm\Rightarrow \lambda =35cm=0.35m$

So, $v=n\lambda \Rightarrow n=\frac{v}{\lambda }=\frac{350}{0.35}=1000Hz$